
Next, we prove (REF ). By the equivalence of Rademacher and Gaussian complexity [1]}, it holds that
\(\mathbb {E}\bigg \Vert n^{-1}\sum _{i=1}^n \varepsilon _i \delta _{X_i}\bigg \Vert _{\mathcal {G}_{\varphi }}\le \sqrt{\frac{\pi }{2}}\mathbb {E}\bigg \Vert n^{-1}\sum _{i=1}^n g_i \delta _{X_i}\bigg \Vert _{\mathcal {G}_{\varphi }} .\) 
